Cremona's table of elliptic curves

6171 = 3 · 11² · 17

Field	Data	Notes
Atkin-Lehner	3- 11- 17+	Signs for the Atkin-Lehner involutions
Class	6171d	Isogeny class
Conductor	6171	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-35715833675577 = -1 · 34 · 1110 · 17	Discriminant
Eigenvalues	1 3-  2  0 11-  2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,8225,-14401]	[a1,a2,a3,a4,a6]
Generators	[31958:2004475:8]	Generators of the group modulo torsion
j	34741712447/20160657	j-invariant
L	6.2934758054669	L(r)(E,1)/r!
Ω	0.38660352643207	Real period
R	4.0697221928813	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	98736bv3 18513r4 561d4 104907l3	Quadratic twists by: -4 -3 -11 17

Hecke Eigenvalues for elliptic curve 6171d4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	-	2	0	-	2	+	-8	-8	-6	8	6	-2	-8	-4	6	-8	-10	4	0	10	0	-12	-14	-14

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Quadratic twists for elliptic curve 6171d4

-4	-3	-11	17
98736bv3	18513r4	561d4	104907l3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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